The large deviations theorem and ergodic sensitivity

Let ( X , d ) be a nontrivial compact metric space and f : X → X a continuous map. In this paper, we introduce the concept of ergodic sensitivity, which is a stronger form of sensitivity. It is shown that if f is a topologically strongly ergodic map satisfying the large deviations theorem then it is ergodically sensitive. In particular, if a continuous map f : T → T is topologically strongly ergodic, then f is cofinitely sensitive and consequently, f is ergodically sensitive, where T is a tree.